Polymorphism and melt in high-pressure tantalum

Abstract

Recent small-cell (< 150-atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal omega (hex-ω) phase more stable than the normal bcc phase at high temperature (T) and pressure (P) above 70 GPa [Burakovsky et al., Phys. Rev. Lett. 104, 255702 (2010)]. Here we examine possible high-T , P polymorphism in Ta with complementary DFT-based model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, which allow accurate treatment of much larger system sizes (up to ~ 80000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hex-ω phases for the high-T , P phase diagram to 420 GPa, studying the mechanical and relative thermodynamic stability of these phases for both small and large computational cells. Our MGPT potentials fully capture the T = 0 DFT energetics of these phases, while MGPT-MD simulations demonstrate that the higher-energy fcc, hcp and hex-ω structures are only mechanically stabilized at high temperature by large, size-dependent, anharmonic vibrational effects, with the stability of the hex-ω phase also being found to be a sensitive function of its c / a ratio. Both twophase and Z-method melting techniques have been used in MGPT-MD simulations to determine relative phase stability and its size dependence. In the large-cell limit, the twophase method yields accurate equilibrium melt curves for all five phases, with bcc producing the highest melt temperatures at all pressures and hence being the most stable phase of those considered. The two-phase bcc melt curve is also in good agreement with dynamic experimental data as well as with the MGPT melt curve calculated from bcc and 2 liquid free energies. In contrast, we find that the Z method produces only an upper bound to the equilibrium melt curve in the large-cell limit. For the bcc and hex-ω structures, however, this is a close upper bound within 5% of the two-phase results, although for the A15, fcc, and hcp structures, the Z-melt curves are 25-35% higher in temperature than the two-phase results. Nonetheless, the Z method has allowed us to study melt size effects in detail. We find these effects to be either small or modest for the cubic bcc, A15, and fcc structures, but to have a large impact on the hexagonal hcp and hex-ω melt curves, which are dramatically pushed above that of bcc for simulation cells less than 150 atoms. The melt size effects are driven by and closely correlated with similar size effects on the mechanical stability and the vibrational anharmonicity. We further show that for the same simulation cell sizes and choice of c / a ratio, the MGPT-MD bcc and hex-ω melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the small-cell limit. But in the large-cell limit, the MGPT-MD hex-ω melt curve is always lowered below that of bcc for any choice of c / a , so bcc is the most stable phase.We conclude that for the non-bcc Ta phases studied, one requires simulation cells of at least 250-500 atoms to be free ...

Shock-induced plasticity in tantalum single crystals: Interatomic potentials and large-scale molecular-dynamics simulations

“…Recent quantum molecular dynamics (QMD) simulations of the melt curve of Ta suggest that for pressures above about 100 GPa, Ta may undergo a phase transition to a hex-ω phase, and the phase diagram of Ta may exhibit a bcc/hex-ω/liquid triple point located around 100 GPa and 250 0K. 2 However, the conclusions drawn from these QMD simulations and the existence of a phase change in Ta at high pressure have been questioned recently by Haskins et al, 3 who argue that the small system sizes associated with the QMD simulations may overestimate the stability of the ω phase relative to the bcc one. The existence of a phase transition (such as the postulated bcc → hex-ω one) at high pressures and temperatures has also been proposed as a way to explain marked differences in the melt line between DAC and shock-wave experiments.…”

Efficient wide-range calculation of free energies in solids and liquids using reversible-scaling molecular dynamics

“…Using quantum-mechanical interatomic potentials obtained from model generalized pseudopotential theory (MGPT) [7][8][9][10][11][12], our free-energy approach applied to liquid and stable solid phases has been successfully used to calculate highpressure melt curves in metals [11,12] at higher accuracy and in a fraction of the time previously required from thermodynamic integration alone [8,9]. We have also extended our method to treat unstable solid phases that are only mechanically stabilized at high temperature by large anharmonic vibrational effects, where such structures become either metastable or stable phases in the high-temperature phase diagram [12]. The purpose of this paper is to elaborate the details of our generalized RSMD free-energy approach, and to illustrate the power and utility of the method through application to the temperaturepressure phase diagram and multiphase equation of state (EOS) of tantalum (Ta).…”

“…12, which addressed the related issue of possible solid-phase polymorphism at high temperatures and pressures in Ta, using dynamic MD simulations via Z-method [13] and two-phase coexistence [12,14] melt techniques to examine the thermodynamic phase stability of candidate solid phases relative to the bcc ground state. A preliminary bcc melt curve for Ta calculated with our RSMD free-energy method was introduced in Ref.…”

“…A preliminary bcc melt curve for Ta calculated with our RSMD free-energy method was introduced in Ref. 12, but it was only used there as a convenient baseline with which to test the accuracy of the Z and two-phase melt methods, with all RSMD-related details and further applications deferred to the present paper. In addition, it was shown in Ref.…”

“…In addition, it was shown in Ref. 12 that the Z method only produces an upper bound to the equilibrium melt curve, while the two-phase method is most accurate and reliable for large MD simulation cells. This underscores the importance of accurate and efficiently calculated free energies in treating the phase diagram and multiphase EOS.…”